Hello, Can anyone give some clue on how I can determine if $\displaystyle R^{Z^+}$ is or isn't connected in the metric topology with distance

$\displaystyle \rho(x,y)=Sup\{\overline{d}(x_i,y_i):i\in Z^+\}$ where

$\displaystyle \overline{d}(a,b)=Min\{|a-b|,1\}$